Parametrization of Y-FTZB is complicated by the random orientations of the FTZB2− linkers (FTZB2− = 2-fluoro-4-(tetrazol-5-yl)benzoate) with respect to the Y3+ ions. The ionic clusters, composing of six metal ions, with each beingcoordinated to four µ3–OH groups to form a roughly spherical [Y6(µ3–OH)8]10+ molecular building block (Figure S1(a)), arewell defined in the X-ray crystal structure of the MOF, with the exception of the unresolved hydrogen atoms whose positionswere determined via geometry optimization. However, the 12 FTZB2− linkers (Figure S1(b)) that are coordinated to eachcluster show considerable positional variation. The linkers are randomly aligned with respect to the functionality (tetrazolateor carboxylate) coordinated to any given set of Y3+ ions, a right/left hand orientation of the fluorine functionality, and tworotational ring positions. This leads to a total of eight distinct occupation sites for a given linker.
(a) (b)
Figure S1. Molecular building blocks of Y-FTZB: (a) [Y6(µ3–OH)8]10+ cluster and (b) FTZB2− linker. Atom colors: C = cyan, H= white, N = blue, O = red, F = yellow, Y = lavender.
For the determination of the atomic positions that are capable of representing the full positionally disordered structure,some sensible approximations were made. In the case of the rotational ring orientations, for which the dihedral angle withregards to the planar carboxylate/tetrazolate alignment is ±4.7◦, the variation was considered to be negligible and theselections were random. While the co-location of single bonded functional groups is consistent with local mobility (i.e.,components capable of rotation), that is not believed to be the case for this structure. Rather, the deviation from theplanarity of the linker is attributed to the optimal low energy accommodation for the fluorine functionality with respect to theneighboring linker functionailties. As such, the two ring orientations are a result of the fluorine disorder and have no capacityto interconvert. This supposition was supported by examining the crystal structure of the MOF, Tb-TZB, referred to ascompound 3 in the work of Xue et al.1 This compound is isostructural with Y-FTZB and possesses the same constituents withthe exception of the metal and the linkers. This MOF consists of TZB2− linkers, which are the unfluorinated counterparts ofthe FTZB2− linkers. In this structure, no deviation from linker planarity was observed, though the linker head orientationremains random. It is considered unlikely that the addition of a highly electronegative fluorine atom with a considerablylarger atomic radius than hydrogen would result in increased linker mobility.
In the case of the left/right hand fluorine orientation, these positional selections were again made randomly. It is expected
that the adjacent fluorine positions are sufficiently distant (approximately 4.5 A for the configuration minimizing the in-terfluorine distance and considerably larger for other alignments) as to make the effect on the electronic structure of theseneighboring linkers negligible. Note, the linker alignment with respect to the [Y6(µ3–OH)8]10+ clusters cannot be dismissedas insignificant. A Y3+ ion that is coordinated to a tetrazolate group will have a different electronic structure than an ionthat is coordinated to a carboxylate group. As each Y3+ ion is coordinated to four linkers, the situation of an ion with onlya single functional group attached to it will be the least probable. The number of possible linker orientational conformationsabout a given metal corresponds to:
ω = CL (1)
where ω is the number of orientational linker combinations, C is the number of conformations for each linker, and Lis the number of linkers coordinated to each ion. This yields a total of 16 possibilities for the MOF studied. However,this number does not account for the symmetry leading to degenerate configurations. A total of six nondegenerate linkerarrangements with respect to a Y3+ ion exist. In the physical crystal structure, an equal a priori probability for any givenconfiguration is assumed. Y3+ ions that are coordinated to 4 tetrazolate or 4 carboxylate groups (here denoted configurations1 and 2, respectively, see Figures S2(a) and S2(b)) are considered non-degenerate states and each have a 1/16 probabilityof observance. Y3+ ions that are coordinated to 3 tetrazolate or 3 carboxylate groups (configurations 3 and 4, respectively,see Figures S2(c) and S2(d)) as well as those with two adjacent linkers of like orientation (configuration 5, see Figure S2(e))each have four–fold degeneracy, resulting in a 4/16 probability of observance apiece. The final configuration with alternatinglinker orientations (configuration 6, see Figure S2(f)) is observed in 2/16 of Y3+ ions.
(a) (b)
(c) (d)
(e) (f)
Figure S2. The six possible linker/Y3+ ion configurations of Y-FTZB: (a) configuration 1, (b) configuration 2, (c) configuration 3,(d) configuration 4, (e) configuration 5, and (f) configuration 6. Atom colors: C = cyan, H = white, N = blue, O = red, F = yellow,Y = lavender.
A unit cell in which all Y3+ ions corresponded to configuration 5 was considered (here denoted structure 1, see FigureS4(a)). Configuration 5 was chosen from the three most frequently observed orientations in order to preserve the symmetryof the crystal structure. This arrangement resulted in two distinct linker-cluster arrangements. In the first, two tripods ofthe tetrazolate oriented linkers exist in diametrically opposed positions on the cluster with a ring of the carboxylate orientedlinkers forming a ring in between them, while the second has carboxylate tripods and a tetrazolate ring (Figure S3). Of thefour clusters extant in a single unit cell, two had the first arrangement and the others had the second.
The positions of the cationic dimethylammonium counterions also had to be determined. Eight of these ions were requiredin one unit cell to balance the charge of the anionic framework. While these ions are resolved in the X-ray crystal structure,
S3
(a) (b)
Figure S3. Two cluster-linker alignments observed in structure 1 with all atoms considered chemically distinguishable. Atom colors:C = cyan, H = white, N = blue, O = red, F = yellow, Y = lavender.
the plethora of sites made available by the observed high symmetry in the positionally disordered crystal structure resultedin considerably more localized ions than the eight predicted. Furthermore, considering the fact that no information about thepreferred environment of the counterions with respect to the disordered functionality could be obtained from the structureand the fact that the X-ray crystal structure was taken prior to activation (thus, raising the possibility of solvent interactioneffecting the sorption site about the counterions), it was decided that the (CH3)2NH2
+ counterions would be separatelyparametrized and the positions were determined via simulated annealing in the canonical ensemble as described below (seeCanonical Monte Carlo section).
While the simulated hydrogen uptake at 77 K and 87 K in this structure is consistent with experiment, the initial isostericheat of adsorption (Qst) value is notably lower. This result is consistent with the existence of a small number of superiorsorption sites in the physical crystal that is not represented in the modeled structure. As a result, a second unit cell (heredenoted structure 2, see Figure S4(b)) was parametrized. In this variant, the same approximations regarding the ring andfluorine orientations were made while the linker configurations about the 24 Y3+ ions were chosen to reflect orientations1, 2, 3, 4, and 6 in the proper probabilistic proportions. Together, the two structures exhibit all possible metal/linkerconformations. Structure 2 produced a similar uptake to structure 1, but with a significantly higher initial H2 Qst value thatis close to the experimental value for Y-FTZB. The primary sorption site to which this value corresponds to consists of aY3+ ion that is coordinated to four tetrazolate functional groups (an alignment only extant in structure 2) and in proximityto a dimethylammonium counterion.
S4
(a) (b)
Figure S4. The a/b/c axis view of the unit cell of (a) structure 1 and (b) structure 2 of Y-FTZB. Structure 2 was used for thesimulations in this work. The (CH3)2NH2
+ counterions are shown in van der Waals representation. Atom colors: C = cyan, H =white, N = blue, O = red, F = yellow, Y = silver.
S5
Parametrization
The potential energy of Y-FTZB is a function of repulsion/dispersion parameters, atomic point partial charges, and atomicpoint polarizabilities that are localized on the nuclear center of all atoms of the MOF. The Lennard-Jones 12–6 potential2
was used to model repulsion/dispersion interactions, and these parameters for all MOF atoms were taken from the UniversalForce Field (UFF).3 The partial charges for the atoms in Y-FTZB were determined from electronic structure calculations onseveral fragments that were taken from the crystal structure of the MOF. More details of these calculations can be found in thenext section. The polarizabilities for all C, H, N, O, and F atoms were taken from a carefully parametrized and transferableset based on the work by van Duijnen and Swart.4 The polarizability parameter for Y3+ was calculated for the isolatedcation using the DFT functional PBE0, the def2-QZVPP basis set with effective core potentials and using the SCF programORCA5 to solve the coupled-perturbed SCF equations. A value of 0.60159 A3 was calculated as the polarizability for Y3+.
S6
Electronic Structure Calculations
The electrostatic environment of Y-FTZB was approximated using partial charges localized on the atomic positions. Thesecharges were determined by perfoming electronic structure calculations on a series of representational fragments that weretaken from the crystal structure of the MOF. Chemical termination was achieved by the addition of hydrogen atoms whereappropriate. Hartree–Fock methods were used to calculate the electrostatic potential surface of each fragment and the partialcharges were fitted to reproduce the potential at a large number of points along the surface using the CHELPG method.6,7
The NWChem simulation package8 was used with the 6-31G∗ basis set applied for all first and second row elements. Thisbasis set has been shown to produce overpolarized charges for gas phase fragments that are consistent with condensed phasemedia.9 For the Y3+ ions, the LANL2DZ10–12 effective core potential basis set was employed for sensible treatment of theinner core electrons of this many-electron species. Discarding terminal atoms whose environments do not approximate MOFconditions, the charges were evaluated for each chemically distinct atom in the fragment. These charges were then averagedover all fragments to obtain the charges that were used in the simulation.
Note, prior to charge fitting, the determination of the chemically distinguishable atoms was required. The positionallydisordered structure of Y-FTZB is highly symmetric, with each Y3+ ion, µ3–OH group, and FTZB2− linker being in achemically indistinguishable location from every other component of its type. This yielded a total of 21 chemically distinctatoms. The selection of linker orientaions as described above breaks down the structural symmetry, leading to a prohibitivelylarge number of positionally distinguishable atoms. As a consequence, the structure was examined to determine psuedo-degenerate atoms, i.e., those in sufficiently similar environments as to make them identical to within simulation precision.
Structure 1, described in the Crystal Configurations section, was considered first. For this higher symmetry crystalstructure, the Y3+ ions are considered interchangeable as the orientation of the central ring of the linker and its attendantfluorine atom are considered sufficiently distant as to have a negligible electrostatic effect on the metal ions. In both clusters,each ion is coordinated to two tetrazolate and two carboxylate groups, thus giving them similar environments. Charge fittingof similar fragments of both cluster types yielded similar charges (Table S1), indicating that this assumption is viable. Becausethere is one linker of similar alignment and two of dissimilar alignment with respect to their Y3+-coordinated functionalgroup, this sensible approximation was made to treat them as interchangable. Additional asymmetric effects from variantcentral ring and/or fluorine orientations are again considered sufficiently distant to be disregarded.
Initially, the µ3–OH groups were consided to be chemically interchangable. However, examination of the fragment chargesrevealed significant alterations in the charge magnitudes depending on the identity of the Y3+-coordinated functional groupssurrounding the hydroxide ion. The charge separation on the hydroxyl oxygen atom for the two extreme situations ofthree carboxylate–metal oriented linkers compared to three tetrazolate–metal oriented linkers is more negative than −1.0 e−
despite the homogeneity of the coordinated metal ions charges (Table S1). As such, the hydroxide ions were divided into fourchemically distinct sets: those surrounded by carboxylate groups, those surrounded by tetrazolate groups, and the two setswith one coordinated carboxylate/tetrazolate and two of the other moiety. Thus, the number of chemically distinct atomsincreased from 21 to 27. Sixteen fragments were selected to give a well averaged value for each chemically distinct atom (FigureS5). The final calculated partial charges for the chemically distinct atoms in structure 1 of Y-FTZB are provided in Table S3.
Parametrization of structure 2, which was undertaken after the failure of structure 1 to accurately model the physicalcrystal (as discussed in the Crystal Configurations section), was a slightly more complex problem. Five distinct Y3+ ions existin structure 2 with respect to the linker coordination environments, none of which correspond to the ion observed in structure1. As expected, examination of fragments containing these ions yielded a wide range of partial charges, with the maximalcharge having more than twice the minimal value and with an absolute magnitude greater than 1.0 e−. Note, the fragmentsthat were selected for structure 2 are shown in Figure S7, and the calculated partial charges for the chemically distinct atomson each fragment can be found in Table S2. The µ3–OH groups in this structure, which are caught between chemically distinctY3+ ions as well as variant linker functionality, produced a new set of dissimilar charges. A total of six different linker/Y3+
environments were identified, with a difference of 0.7 e− observed between the high and low hydroxyl oxygen charges.While less homogenously arranged than their counterparts in structure 1 (since the linkers have non-identical Y3+ coor-
dination and attendant nearby functionality in structure 2), the partial charges for the atoms on the linkers in structure 2are consistent with their counterparts in structure 1 to within joint uncertainties. As such, all linkers in both structures areconsidered interchangable and, in the interest of maintaining consistency, the partial charges that were determined for thefragments of structure 1 applied to those corresponding to structure 2. A total of 17 chemically distinct atoms (Figure S6)(five Y3+ ions and six µ3–OH groups) were added to the total number of chemically distinct atoms to give a total of 44.Structures 1 and 2 contain 27 and 35 of these atoms, respectively. The partial charges for the 17 chemically distinguish-able atoms observed in structure 2 of Y-FTZB can be found in Table S4. Note, as explained in the Crystal Configurationssection, the dimethylammonium counterion was parametrized separately from the framework. The partial charges for thechemically distinct atoms on the (CH3)2NH2
+ counterions (Figure S8) are provided in Table S5. These charges were usedfor the counterions in the simulations in both structures.
S7
Table S1. Comparison of partial charges (e−) for the series of fragments taken from structure 1 of Y-FTZB. Numbering of atomscorresponds to Figure S3.
Figure S5. Fragments of structure 1 of Y-FTZB that were selected for charge fitting calculations. Atom colors: C = cyan, H = white,N = blue, O = red, F = yellow, Y = lavender.
(a)Fragment 1 (b)Fragment 2 (c)Fragment 3
(d)Fragment 4 (e)Fragment 5 (f)Fragment 6
(g)Fragment 7 (h)Fragment 8 (i)Fragment 9
S9
(j)Fragment 10 (k)Fragment 11 (l)Fragment 12
(m)Fragment 13 (n)Fragment 14 (o)Fragment 15
(p)Fragment 16
S10
Figure S6. Four [Y6(µ3–OH)8(FTZB)12]14− clusters observed in structure 2 of Y-FTZB. Numerical labeling correspond to chemicallydistinct atoms not observed in structure 1. Atom colors: C = cyan, H = white, N= blue, O = red, F = yellow, Y = lavender.
(a)Cluster 1 (b)Cluster 2
(c)Cluster 3 (d)Cluster 4
S11
Figure S7. Fragments of structure 2 of Y-FTZB that were selected for gas phase charge fitting calculations. Numerical labelingcorrespond to chemically distinct atoms evaluated. Atom colors: C = cyan, H = white, N = blue, O = red, F = yellow, Y = lavender.
(a)Fragment 1 (b)Fragment 2 (c)Fragment 3
(d)Fragment 4 (e)Fragment 5 (f)Fragment 6
(g)Fragment 7 (h)Fragment 8
S12
(i)Fragment 9 (j)Fragment 10 (k)Fragment 11
(l)Fragment 12 (m)Fragment 13 (n)Fragment 14
(o)Fragment 15 (p)Fragment 16
S13
Figure S8. The numbering of the chemically distinct atoms on the (CH3)2NH2+ counterion as referred to in Table S5. Atom colors:
C = cyan, H = white, N = blue.
Table S3. Partial charges (e−) for the chemically distinct atoms in structrure 1 of Y-FTZB. Numbering of atoms corresponds toFigure S3.
Atom Label q (e−)
Y 1 1.55352
O 2 -0.27106
H 3 0.09906
O 4 -0.90386
H 5 0.21148
O 6 -0.59791
H 7 0.16238
O 8 -1.34975
H 9 0.29320
O 10 -0.70575
O 11 -0.76238
C 12 0.96988
C 13 -0.17176
C 14 0.36353
F 15 -0.25665
C 16 -0.12147
H 17 0.16105
C 18 -0.15842
H 19 0.14400
C 20 -0.07465
H 21 0.09865
C 22 -0.29243
C 23 0.89536
N 24 -0.67027
N 25 -0.67746
N 26 0.05780
N 27 0.08283
S14
Table S4. Partial charges (e−) for the chemically distinct atoms that exist only in structure 2 of Y-FTZB. The partial charges forthe atoms on the linkers are consistent with those reported in Table S3 for structure 1. Numbering of atoms corresponds to Figure S6.
Atom Label q (e−)
Y 1 1.03055
Y 2 1.24881
Y 3 1.67598
Y 4 1.90324
Y 5 2.29367
O 6 -0.79045
H 7 0.07007
O 8 -0.39103
H 9 0.00082
O 10 -1.01268
H 11 0.20248
O 12 -0.57063
H 13 0.12194
O 14 -1.06909
H 15 0.26951
O 16 -0.75113
H 17 0.24573
Table S5. Partial charges (e−) for the chemically distinct atoms on the the (CH3)2NH2+ counterion. Numbering of atoms corresponds
to Figure S8.
Atom Label q (e−)
N 1 0.20260
C 2 -0.19430
H 3 0.22290
H 4 0.12150
H 5 0.12430
S15
H2 Potential
Table S6. Parameters used to characterize the five–site polarizable H2 potential13 used in this work. COM corresponds to the center-of-mass site, H corresponds to the atomic locations of the hydrogen atoms, and OS corresponds to the Lennard-Jones off-site.
Site r(A) ε(K) σ(A) q (e−) α◦(A3)
COM 0.00000 12.76532 3.15528 -0.74640 0.69380
H 0.37100 0.00000 0.00000 0.37320 0.00044
H -0.37100 0.00000 0.00000 0.37320 0.00044
OS 0.36300 2.16726 2.37031 0.00000 0.00000
OS -0.36300 2.16726 2.37031 0.00000 0.00000
S16
Canonical Monte Carlo
While the eight (CH3)2NH2+ counterions required to neutralize the anionic unit cell were sufficiently immobile to resolve
in the crystal structure, these positions were highly disordered as the corresponding CIF file for Y-FTZB (taken fromreference 1) reported an occupancy of 0.13 for any of the possible localities. Additionally, the structure was examined priorto activation, as the interactions between the counterions and the solvent molecules could have an effect on the locationof the counterions. As a result, for the determination of the counterion positions, these ions were separately parametrizedwith Lennard-Jones parameters taken from UFF,3 point polarizabilities taken from van Duijnen and Swart,4 and partialcharge taken from a single ion charge fit using the same methods for the MOF fragments as described earlier (see ElectronicStructure Calculations section).
Canonical Monte Carlo simulations (CMC) were performed in both structures 1 and 2 of Y-FTZB (see Crystal Config-urations section), with each containing eight mobile dimethyammonium counterions. This method constrains the particlenumber (N), volume (V ), and temperature (T ) of the simulation cell to be constant. These simulations were executed withthe Massively Parallel Monte Carlo (MPMC) code.14 The equilibrium positions of the counterions in both structures weredetermined using simulated annealing. An initial temperature of 500 K was used in order to encourage the ions to explorethe systems prior to settling into the minima. Due to the highly variable sorption environement in this MOF, especiallyfor structure 2, the annealed positions were then used as initial positions for new simulated annealing runs in an attemptto avoid settling into the local minima. This was continued for several iterations with lower energy positions retained andhigher energy positions disregarded to obtain the lowest possible energy. Once these sites were determined, the positions ofthe dimethylammonium counterions were held rigid for the simulations of H2 sorption in Y-FTZB as described in the GrandCanonical Monte Carlo section below.
In both structures, the eight dimethylammonium counterions were initially located in the centers of the tetrahedral cagesof the MOF. Simulated annealing calculations in structure 1 revealed that these counterions settled into the corners formedby a tripod of tetrazolate groups (existing in four cages) and two tetrazolate/one carboxylate corners otherwise (FigureS4(a)). Structure 2 had a predictably less well-ordered result, with four counterions localized in the tetrazolate tripods, twocounterions localized in the 2 tetrazolate/1 carboxylate tripods (again, in cages without the former functionality), and twocounterions localized in proximity to the open-metal sites (Figure S4(b)). Specifically, the latter two counterions positionednear the Y3+ ions that are coordinated to three tetrazolate and one carboxylate moieties, which are labeled atom 2 in FigureS6. Notably, a number of metal sites with this linker coordination remain open for sorbate interactions.
S17
Grand Canonical Monte Carlo
Simulations of H2 sorption in Y-FTZB were performed using grand canonical Monte Carlo (GCMC) in a single unitcell of the MOF. This method constrains the chemical potential (µ), volume (V ), and temperature (T ) of the MOF–H2
system to be constant while allowing other thermodynamic quantities to fluctuate.15 The simulation involves the randominsertion/deletion and movement of sorbate molecules within the simulation box until equilibrium is reached. An infinitelyextended crystal environment was approximated by periodic boundary conditions with a spherical cut-off of 11.71825 A,which corresponds to half the unit cell dimension length. All MOF atoms were constrained to be rigid for the simulations,including the atoms of the dimethylammonium counterions. The average particle number was calculated numerically by astatistical mechanical expression based on the grand canonical ensemble.16,17 The chemical potential for H2 was determinedusing the BACK equation of state.18 Quantum corrections were included in the simulations by using the Feynman-Hibbspotential to the fourth order.19 All simulations were performed using the Massively Parallel Monte Carlo (MPMC) code, anopen-source code that is currently available for download on Google Code.14
S18
Many-Body Polarization
An overview of the Thole-Applequist type polarization model20–22 used in this work is given here. The induced dipole, µ,at site i can be calculated using the following equation:
~µi = α◦i
~Estati −N∑j 6=i
Tij~µj
(2)
where α◦i represents the (scalar) atomic point polarizability, ~Estati is the static electric field experienced at site i due to
the presence of the MOF atoms and the H2 molecules, ~µj represents the induced dipole at site j, and Tαβij is the dipole field
tensor which is defined from electrostatic first-principles as the following:20
Tαβij = ∇α∇β 1
rij(3)
=δαβ
r3ij− 3xαxβ
r5ij(4)
where rij is the distance between sites i and j. Equation 2 is a self-consistent equation with respect to the dipoles andthus, the quantity ~µi must be solved for using iterative methods for large systems. Note, equation 2 can be solved exactlyusing matrix inversion, but this is computationally efficient for only small systems. The iterative method employed hereinwas the Gauss–Seidel relaxation technique.23 This method consists of updating the current dipole vector set for the kth
iteration step as the new dipole vectors become available via the following:24
~µki = α◦i
~Estati −∑j 6=i
Tij~µk−1+ζj
(5)
ζ =
{0, if i < j
1, if i > j(6)
In this equation, Tij is the modified dipole field tensor that accounts for short range divergences in the polarization model,defined as:24–26
Tαβij =δαβr3ij
[1−
(λ2r2ij
2+ λrij + 1
)e−λrij
]− 3xαxβ
r5ij
[1−
(λ3r3ij
6+λ2r2ij
2+ λrij + 1
)e−λrij
](7)
where λ is a parameter damping the dipole interactions near the regions of discontinuity. A value of 2.1304 was used for λin this work, which is consistent with the work performed by B. Thole.21 The many-body polarization energy for the MOF–H2 system was calculated by the following based on the work of Palmo and Krimm:27
Ukpol = −1
2
∑i
~µki · ~Estati − 1
2
∑i
~µki · ~Ek+1i (8)
Thus, the polarization energy was determined from the kth iteration dipoles and the (k + 1)th induced field.
S19
Inelastic Neutron Scattering Details
Y-FTZB was synthesized and activated according to the procedure reported by Xue et al.1 The inelastic neutron scattering(INS) spectra for Y-FTZB were collected on the cold neutron time-of-flight spectrometer TOFTOF (at the FRM-II, Munich,Germany) using 0.682 g of the compound. The activated sample was transferred under He into the Al sample holder usedfor the experiment. The sample holder was attached to the sample stick of the cryostat, connected to a capillary leading toan external gas handling system, and evacuated. Sorption of predetermined amounts of H2 was carried out in situ at 77 Kfrom the external gas handling system, and the INS spectra were collected at a temperature of 1.5 K. The incident energieschosen in these measurements were 25 meV and 9.1 meV, to (respectively) cover a wide range of energy transfers in energyloss, and to resolve the most interesting features in the low energy transfer region. The resulting high resolution (λ = 3.0A) and low resolution spectrum (λ = 1.8 A) at a loading of 2 H2/Y are provided in Figures S9(a) and S9(b), respectively.The high resolution spectra for different loadings of H2 are shown in Figure S10.
As explained in the main text, the peak 2.4 meV in the INS spectrum for Y-FTZB corresponds to sorption onto a Y3+
ion that is surrounded by four tetrazolate groups and in proximity to a (CH3)2NH2+ counterion. While the most interesting
feature in the INS spectrum for Y-FTZB is the peak that appears at 2.4 meV, the sorption sites that give rise to the peaksat approximately 4.0 and 9.0 meV, respectively, have been identified through our simulations. The 4.0 meV peak observedin the INS spectrum corresponds to sorption onto the other chemically distinct Y3+ ions in the structure. Although theenergetics about these sorption sites are not as strong as the most favorable binding site in the MOF due to the lack ofall four surrounding tetrazolate groups and proximal (CH3)2NH2
+ counterion, the rotational transition for this site is stilllower than the lowest energy peak for most existing MOFs (see next section, Table S7). In addition, according to thephenomenological model,28 a rotational barrier of 57.6 meV can be associated with the 4.0 meV peak. Even this barrierheight is higher than those for MOFs with open-metal Cu2+ ions and MOFs that are part of the M-MOF-74 series (TableS7). The peak at approximately 9.0 meV in the INS spectrum as observed in Figure S9(b) corresponds to the sorption ofH2 in the corners of the tetrahedral cage and in proximity to the (CH3)2NH2
+ counterions. Although it was observed thatH2 molecules sorbed about uncoordinated counterions have low rotational transitions29,30 the (CH3)2NH2
+ ion is notablybulky and the lower charge/size ratio of this ion results in lower rotational barriers for the sorbed hydrogen. Calculation ofthe rotational energy levels for a H2 molecule sorbed in proximity to a counterion revealed a transition in the range of 9.0 to10.0 meV. This rotational tunneling transition is comparable to those for MOFs that have open-metal Cu2+ ions.31,32
S20
(a)
(b)
Figure S9. Inelastic neutron scattering (INS) spectra for hydrogen in Y-FTZB at a loading of 2 H2/Y. (a) High resolution spectrumcollected with an incident wavelength of 3.0 A. (b) Low resolution spectrum collected with an incident wavelength of 1.8 A.
Figure S10. The high resolution inelastic neutron scattering (INS) spectra for hydrogen in Y-FTZB at different loadings: 1 mmol H2
(black), 2 mmol H2 (red), 4.2 mmol H2 (violet), and 6 mmol H2 (blue). The spectra were collected with an incident wavelength of 3.0 A.
S21
Comparison of Rotational Barriers
Table S7. A comparison of the lowest energy peaks (0 to 1 transition for the strongest sorption site) observed in the INS spectra forH2 in various porous materials and their corresponding rotational barriers as calculated using the model in reference 28. The valuesin parentheses were calculated using a theoretical potential energy surface.
Porous Material Lowest Energy Peak (meV) Rotational Barrier (meV) Reference
LiA 0.85 121.1 33
LiX 1.8 90.1 33
NaX 2.3 79.7 33
Y-FTZB 2.4 78.3 (85.77) This work
Li-rho-ZMOF 3.0 69.5 29
NaA 3.6 62.0 33
DMA-rho-ZMOF 4.3 54.4 29
In-soc-MOF 4.8 50.0 34
rht-MOF-1 5.0 48.7 30
SIFSIX-2-Cu-i 5.6 47.7 (45.86) 35
Ni-MOF-74 6.6 37.7 36
Mg-MOF-74 6.7/6.8 37.0/36.0 36/37
rht-MOF-7 6.8 36.0 38
Mg-rho-ZMOF 7.2 35.3 29
Co-MOF-74 7.7 31.0 36
PCN-12 7.7 31.0 32
Zn-MOF-74 8.3 28.0 (27) 39 (40)
PCN-6 8.7 25.8 41
PCN-6′ 8.85 25.0 41
IRMOF-11 8.9 24.8 42
rht-MOF-4a 9.0 24.0 43
HKUST-1 9.1 23.7 31
MOF-177 9.7 20.4 42
SIFSIX-2-Cu 10.5 17.0 35
IRMOF-8 10.8 15.6 42
S22
Quantum Rotation Calculations
The two-dimensional quantum rotational levels for a H2 molecule sorbed at a sorption site in Y-FTZB were calculated bydiagonalizing the rotor Hamiltonian in the spherical harmonic basis, Yjm, which is the following:
H = Bj2 + V (θ, φ) (9)
where B is the rotational constant for molecular hydrogen, which is equal to approximately 85.35 K,44 j2 is the angularmomentum operator, and V (θ,φ) is the potential energy surface for the rotation of the H2 molecule with its center-of-massheld fixed within the MOF–H2 system. Each matrix element, 〈Yjm|V (θ,φ)|Yjm〉, was constructed using Gauss-Legendrequadrature45 with a basis set consisting of ±m functions.24 The matrix was diagonalized using the LAPACK linear algebrapackage,46 yielding the rotational energy eigenvalues and the eigenvector coefficients. The two-dimensional rotational levelswere calculated with j = 7, leading to 64 basis functions. The calculated rotational levels for a H2 molecule sorbed aboutthe most favorable sorption site in Y-FTZB are provided in Table S8.
The rotational barrier was determined by calculating the potential energy of the MOM–H2 system as the H2 molecule isrotated at various angles of θ (0 to 180◦) and φ (0 to 360◦). Single point energies were obtained on a sphere (4,096 pointsbased on 64 × 64 Gaussian quadrature integration) and the rotational barrier was calculated by taking the difference betweenthe high and low values. All calculations were performed using the Massively Parallel Monte Carlo (MPMC) code, which iscurrently available for download on Google Code.14
Table S8. The calculated two-dimensional quantum rotational levels for a H2 molecule sorbed about the most favorable sorption sitein Y-FTZB as shown in Figure 3 in the main text. Relative energies are given in meV.
n j Calc. ∆E (meV)
1 0 0.00
2 2.74
3 1 24.65
4 40.44
5 44.59
6 46.45
7 2 54.60
8 72.85
9 83.45
S23
1 Xue, D.-X.; Cairns, A. J.; Belmabkhout, Y.; Wojtas, L.; Liu, Y.; Alkordi, M. H.; Eddaoudi, M. Journal of the American ChemicalSociety 2013, 135, 7660–7667.
2 Jones, J. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 1924,106, 463–477.
3 Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. Journal of the American Chemical Society 1992, 114,10024–10035.
4 van Duijnen, P. T.; Swart, M. The Journal of Physical Chemistry A 1998, 102, 2399–2407.5 Neese, F. Wiley Interdisciplinary Reviews: Computational Molecular Science 2012, 2, 73–78.6 Chirlian, L. E.; Francl, M. M. Journal of Computational Chemistry 1987, 8, 894–905.7 Breneman, C. M.; Wiberg, K. B. Journal of Computational Chemistry 1990, 11, 361–373.8 Valiev, M.; Bylaska, E.; Govind, N.; Kowalski, K.; Straatsma, T.; Dam, H. V.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T.;
de Jong, W. Computer Physics Communications 2010, 181, 1477–1489.9 Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.;
Kollman, P. A. Journal of the American Chemical Society 1995, 117, 5179–5197.10 Stevens, W. J.; Basch, H.; Krauss, M. Journal of Chemical Physics 1984, 81, 6026–6033.11 Hay, P. J.; Wadt, W. R. Journal of Chemical Physics 1985, 82, 270–283.12 LaJohn, L. A.; Christiansen, P. A.; Ross, R. B.; Atashroo, T.; Ermler, W. C. Journal of Chemical Physics 1987, 87, 2812–2824.13 Belof, J. L.; Stern, A. C.; Space, B. Journal of Chemical Theory and Computation 2008, 4, 1332–1337.14 Belof, J. L.; Space, B. Massively Parallel Monte Carlo (MPMC). Available on Google Code, 2012.15 Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. Physics Letters B 1953, 21, 1087–1092.16 McQuarrie, D. A. Statistical Mechanics; University Science Books: Sausalito, CA, 2000; pp. 53.17 Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Academic Press: New York, 2002;
pp. 129.18 Boublık, T. Fluid Phase Equilibria 2005, 240, 96–100.19 Feynman, R. P.; Hibbs, A. R. Quantum Mechanics and Path Integrals; McGraw-Hill: New York, 1965; pp. 281.20 Applequist, J.; Carl, J. R.; Fung, K.-K. Journal of the American Chemical Society 1972, 94, 2952–2960.21 Thole, B. Chemical Physics 1981, 59, 341 – 350.22 Bode, K. A.; Applequist, J. The Journal of Physical Chemistry 1996, 100, 17820–17824.23 Dinh, T.-L.; Huber, G. A. Journal of Mathematical Modelling and Algorithms 2005, 4, 111–128.24 Belof, J. L. Theory and simulation of metal-organic materials and biomolecules. Ph.D. thesis, University of South Florida, 2009.25 Belof, J. L.; Stern, A. C.; Eddaoudi, M.; Space, B. Journal of the American Chemical Society 2007, 129, 15202–15210, PMID:
17999501.26 Forrest, K. A.; Pham, T.; McLaughlin, K.; Belof, J. L.; Stern, A. C.; Zaworotko, M. J.; Space, B. The Journal of Physical Chemistry
C 2012, 116, 15538–15549.27 Palmo, K.; Krimm, S. Chemical Physics Letters 2004, 395, 133–137.28 Nicol, J. M.; Eckert, J.; Howard, J. The Journal of Physical Chemistry 1988, 92, 7117–7121.29 Nouar, F.; Eckert, J.; Eubank, J. F.; Forster, P.; Eddaoudi, M. Journal of the American Chemical Society 2009, 131, 2864–2870,
PMID: 19206515.30 Pham, T.; Forrest, K. A.; Hogan, A.; McLaughlin, K.; Belof, J. L.; Eckert, J.; Space, B. Journal of Materials Chemistry A 2014,
2, 2088–2100.31 Brown, C. M.; Liu, Y.; Yildirim, T.; Peterson, V. K.; Kepert, C. J. Nanotechnology 2009, 20, 204025.32 Wang, X.-S.; Ma, S.; Forster, P.; Yuan, D.; Eckert, J.; Lopez, J.; Murphy, B.; Parise, J.; Zhou, H.-C. Angewandte Chemie Interna-
tional Edition 2008, 47, 7263–7266.33 Eckert, J.; Trouw, F. R.; Mojet, B.; Forster, P.; Lobo, R. Journal of Nanoscience and Nanotechnology 2010, 10, 49–59.34 Liu, Y.; Eubank, J. F.; Cairns, A. J.; Eckert, J.; Kravtsov, V. C.; Luebke, R.; Eddaoudi, M. Angewandte Chemie International
Edition 2007, 46, 3278–3283.35 Nugent, P.; Pham, T.; McLaughlin, K.; Georgiev, P. A.; Lohstroh, W.; Embs, J. P.; Zaworotko, M. J.; Space, B.; Eckert, J. Journal
of Materials Chemistry A 2014, DOI: 10.1039/c4ta02171a.36 Dietzel, P. D. C.; Georgiev, P. A.; Eckert, J.; Blom, R.; Strassle, T.; Unruh, T. Chemical Communications 2010, 46, 4962–4964.37 Sumida, K.; Brown, C. M.; Herm, Z. R.; Chavan, S.; Bordiga, S.; Long, J. R. Chemical Communications 2011, 47, 1157–1159.38 Pham, T.; Forrest, K. A.; Eckert, J.; Georgiev, P. A.; Mullen, A.; Luebke, R.; Cairns, A. J.; Belmabkhout, Y.; Eubank, J. F.;
McLaughlin, K.; Lohstroh, W.; Eddaoudi, M.; Space, B. The Journal of Physical Chemistry C 2014, 118, 439–456.39 Liu, Y.; Kabbour, H.; Brown, C. M.; Neumann, D. A.; Ahn, C. C. Langmuir 2008, 24, 4772–4777.40 Kong, L.; Roman-Perez, G.; Soler, J. M.; Langreth, D. C. Physical Review Letters 2009, 103, 096103.41 Ma, S.; Eckert, J.; Forster, P. M.; Yoon, J. W.; Hwang, Y. K.; Chang, J.-S.; Collier, C. D.; Parise, J. B.; Zhou, H.-C. Journal of the
American Chemical Society 2008, 130, 15896–15902.42 Rowsell, J. L. C.; Eckert, J.; Yaghi, O. M. Journal of the American Chemical Society 2005, 127, 14904–14910, PMID: 16231946.43 Eubank, J. F.; Nouar, F.; Luebke, R.; Cairns, A. J.; Wojtas, L.; Alkordi, M.; Bousquet, T.; Hight, M. R.; Eckert, J.; Embs, J. P.;
Georgiev, P. A.; Eddaoudi, M. Angewandte Chemie International Edition 2012, 51, 10099–10103.44 Bigeleisen, J.; Mayer, M. G. Journal of Chemical Physics 1947, 15, 261.45 Abramowitz, M. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1965, Chapt. 25, Sect. 4,
Sorensen, D. LAPACK: A portable linear algebra library for high-performance computers. Proceedings of the 1990 ACM/IEEEconference on Supercomputing. 1990; pp 2–11.
